The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several ge...The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume,which can be seen as the higher-dimensional generalization of the pseudo-sphere.展开更多
基金Peking University for providing financial support for the first author
文摘The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume,which can be seen as the higher-dimensional generalization of the pseudo-sphere.
